The Bruhat rank of a binary symmetric staircase pattern

Abstract

In this work we show that the Bruhat rank of a symmetric (0,1)-matrix of order n with a staircase pattern, total support, and containing In, is at most 2. Several other related questions are also discussed. Some illustrative examples are presented.

Keywords

• permutation matrix
• bruhat order
• bruhat shadow
• bruhat rank
• inversion
• 05b20
• 06a07
• 15a36